Information sets from defining sets for Reed-Muller codes of first and second order

Reed-Muller codes belong to the family of affine-invariant codes. As such codes they have a defining set that determines them uniquely, and they are extensions of cyclic group codes. In this paper we identify those cyclic codes with multidimensional abelian codes and we use the techniques introduced...

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Bibliographic Details
Published in:arXiv.org 2024-01
Main Authors: Bernal, José Joaquín, Juan Jacobo Simón
Format: Article
Language:English
Online Access:Get full text
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Summary:Reed-Muller codes belong to the family of affine-invariant codes. As such codes they have a defining set that determines them uniquely, and they are extensions of cyclic group codes. In this paper we identify those cyclic codes with multidimensional abelian codes and we use the techniques introduced in \cite{BS} to construct information sets for them from their defining set. For first and second order Reed-Muller codes, we describe a direct method to construct information sets in terms of their basic parameters.
ISSN:2331-8422
DOI:10.48550/arxiv.2401.10109